Bear recently studied the depth first traversal of a Tree in his Data Structure class. He learnt the following algorithm for doing a dfs on a tree.

void dfs(int v,int p){
    vis[v] = 1;
    for(int i=0;i<G[v].size();++i){
        if(G[v][i]!=p)
            dfs(G[v][i],v);
    }
}

Now he was given an array A, Tree G as an adjacency list and Q queries to answer on the following modified algorithm as an homework.

void dfs(int v,int p){
    vis[v] += 1;
    for(int j=1;j<=A[v];++j){
        for(int i=0;i<G[v].size();++i){
            if(G[v][i]!=p)
                dfs(G[v][i],v);
        }
    }
}

The Q queries can be of the following two types :

• \(1\space v\space x\) : Update \(A[v] = x\). Note that updates are permanent.
• \(2\space v\) : Initialize \(vis[u] = 0 \space \forall \space u \in [1,N]\). Run the above algorithm with call dfs(1,-1). Compute the sum \(\large\displaystyle \sum_{u \in Subtree\space of\space v}^v vis[u]\). As the result may be quite large print it \(mod\space 10^9+7\)

INPUT
The first line contains two integers N and Q, the number of vertices in the tree and the number of queries respectively.
Next \(N-1\) lines contains the undirected edges of the tree.
The next lines contains N integers denoting the elements of array A.
Following Q lines describe the queries.

OUTPUT
For each query of type 2, print the required result \(mod\space 10^9+7\).

CONSTRAINT
\(1 ≤ N, Q ≤ 10^5\)
\(1 ≤ A[v],\space x ≤ 10^9\)
\(1 ≤ v ≤ N\)